Application of biorthogonal interpolating wavelets to the Galerkin scheme of time dependent Maxwell's equations

Abstract

A family of biorthogonal interpolating wavelets has been applied to time-domain electromagnetic field modeling through the wavelet-Galerkin scheme. The scaling functions are the Deslauriers-Dubuc interpolating functions and the wavelets are the shifted and contracted version of the scaling functions. This set of bases yields a simple algorithm for the solution of Maxwell's equations in time domain due to their interpolation properties. The derivation of the algorithm is presented in this paper, followed by a series of numerical verifications on some resonant structures.